Although the concept of emergence has become very popular in the last few decades in connection with the development of chaos and complexity theories, it is actually a very old idea, dating at least to the nineteenth century, with some hints of it in ancient and medieval philosophy.

John Stuart Mill discusses the Laws of Nature in his System of Logic, Book III, chapter IV and describes the Law of Universal Causation in chapter V ("The truth that every fact which has a beginning has a cause"). Then, in chapter VI, Mill explores the "Composition of Causes" in mechanics where the parallelogram of two vector forces explains the resultant force. However, this simple principle from dynamics, says Mill, does not apply to materialist chemistry nor to more complex biological life.

Although Mill did not use the term "emergent," he makes the concept clear enough:

This principle [of simple composition], however, by no means prevails in all departments of the
field of nature. The chemical combination of two substances produces, as is
well known, a third substance with properties different from those of either
of the two substances separately, or of both of them taken together. Not a
trace of the properties of hydrogen or of oxygen is observable in those of
their compound, water. The taste of sugar of lead is not the sum of the tastes
of its component elements, acetic acid and lead or its oxide; nor is the colour
blue vitriol a mixture of the colours of sulphuric acid and copper. This
explains why mechanics is a deductive or demonstrative science, and chemistry not. In the one, we can compute the effects of m combinations of causes,
whether real or hypothetical, from the laws which we know to govern those
causes when acting separately; because they continue to observe the same
laws when in combination which they observed when separate: whatever
could have happened in consequence of each cause taken by itself, happens
when they are together, and we have only to "cast up" the results. Not so in
the phenomena which are the peculiar subject of the science of chemistry.
There, most of the uniformities to which the causes conformed when separate cease altogether when they are conjoined; and we are not, at least in the
present state of our knowledge, able to foresee what result will follow from
any new combination, until we have tried the specific experiment.

If this be true of chemical combinations, it is still more true of those far
more complex combinations of elements which constitute organized bodies;
and in which those extraordinary new uniformities arise, which are called the
laws of life. All organized bodies are composed of parts similar to those
composing inorganic nature, and which have even themselves existed in an
organic state; but the phenomena of life, which result from the juxtaposition of those parts in a certain manner, bear no analogy to any of the
effects which would be produced by the action of the component substances
considered as mere physical agents.

(A System of Logic, Book III, chapter VI)

George Henry Lewes also used Mill's example of the properties of water not being reducible to those of oxygen and hydrogen. If all effects are only the consequences of their components, everything would be completely determined by mathematical laws, he said, and then coined the term "emergent":

Although each effect is the resultant of its components, the product of its factors, we cannot always trace the steps of the process, so as to see in the product the mode of operation of each factor. In the latter case, I propose to call the effect an emergent. It arises out of the combined agencies, but in a form which does not display the agents in action.

(Problems of Life and Mind (1875), vol. 2, p. 412)

In his 1912 book Instinct and Experience, C. Lloyd Morgan revived the term "emergent".

In his 1920 book Space, Time, and Deity Samuel Alexander initially cited Lloyd Morgan as the source of emergentism, but Lloyd Morgan reminded Alexander about Lewes' 1875 work. Alexander wrote:

much of what I have to say has been already said by Mr. Lloyd Morgan in the
concluding chapter of his work on Instinct and Experience. The argument is that mind has certain specific characters to which there is or even can be no neural counterpart. It is not enough to say that there is no mechanical
counterpart, for the neural structure is not mechanical
but physiological and has life. Mind is, according to our
interpretation of the facts, an 'emergent' from life, and
life an emergent from a lower physico-chemical level of
existence. It may well be that, as some think, life itself
implies some independent entity and is indeed only mind
in a lower form. But this is a different question, which
does not concern us yet.If life is mind, and is a non-physical entity, arguments derived from the conscious features of mind are at best only corroborative, and it is
an inconvenience in these discussions that the two sets
of arguments are sometimes combined. Accordingly. I
may neglect such considerations as the selectiveness of
mind which it shares with all vital structures.

...in the physical world emergence is no less exemplified in the advent of each new kind of atom, and of each new kind of molecule. It is beyond the wit of man to number the instances of emergence. But if nothing new emerge - if there be only regrouping of pre-existing events and nothing more - then there is no emergent evolution.

Such emergence of the new is now widely accepted where life and mind are concerned. It is a doctrine untiringly advocated by Professor Bergson.

One could not foretell the emergent character of vital events from the fullest possible knowledge of physico-chemical events only...Such is the hypothesis of emergent evolution.

Under emergent evolution there is progressive development of stuff which becomes new stuff in virtue of the higher status to which it has become raised under some supervenient kind of substantial gotogetherness.

(Emergent Evolution (1923), pp. 1-6)

But Lloyd Morgan's idea of emergent novelty may have been an epistemic rather than an ontological claim. The laws of nature may still pre-determine all the higher-level properties, though our understanding of the laws may not be enough to allow us to predict the higher levels:

May we bring emergence itself under the rubric of causation?...Is emergent evolution itself the expression of an orderly and progressive development? If so (and such is my contention), then emergence itself takes rank, as Mill and Lewes also contended, among the "laws of nature." We may be unable to predict the probable nature of a character that is emergently new. We could not have foretold on the basis of physico-chemical events only what the nature of life would be. But that is due to our ignorance before the event of the law of its emergence. May we then, say:

...That such novelty is for us unpredictable owing to our partial knowledge of the plan of emergence up to date, and our necessary ignorance of what the further development of that plan will be.

(Emergent Evolution (1923), p. 281-2)

Vitalists like Henri Bergson and Hans Driesch may not have used the term emergence, but they strongly supported the idea of teleological (purposeful), likely non-physical causes, without which they thought that life and mind could not have emerged from physical matter.

Emergence supports the idea of mental causation in particular and the more general problem of downward causation, for example the downward control of the motions of a cell's atoms and molecules by supervening on biological macromolecules. Is the molecular biology of a cell reducible to the laws governing the motions of its component molecules, or are there emergent laws governing motions at the cellular level, the organ level, the organism level, and so on up to the mental level?

The locus classicus of recent discussions of mental causation is Donald Davidson's 1970 essay "Mental Events," which was revisited in his 1993 essay, "Thinking Causes," published together with 15 critical essays on Davidson's work in the 1993 book Mental Causation, edited by John Heil and Alfred Mele.

That causal relations are normally backed by strict (deterministic) laws

But that there are no such strict laws for mental events acting on physical events

Davidson's goal is to deny the reducibility of mental events to physical events in the lower levels, even to deny the physicist's claim that the motions of the atoms and molecules at the lowest level are causally determinative of everything that happens at higher levels.

Information is neither matter nor energy. It is sometimes embodied in matter and sometimes is communicated as pure energy. It is the scientific basis for an immaterial, non-physical mind that can nevertheless affect the physical world. Information is the modern spirit.

Jaegwon Kim says that Davidson's goal of "non-reductive physicalism" is simply not possible. The physical world is "causally closed," says Kim:

what options are there if we set aside the physicalist picture?
Leaving physicalism behind is to abandon ontological physicalism, the view that bits of matter and their aggregates in space-time exhaust the contents of the world. This means that one
would be embracing an ontology that posits entities other than
material substances — that is, immaterial minds, or souls, outside
physical space, with immaterial, nonphysical properties.

(Physicalism, or Something Near Enough, p. 71)

Kim diagrams Davidson's view of mental events supervening on physical events, to illustrate Kim's claim that having both mental and physical causes would be "overdetermination" and thus one is redundant and must be excluded.

M1

M2

supervenes
on

supervenes
on

P1

- causes -

P2

By causal closure of the physical world, Kim says it is the mental events that are superfluous and must go. (Physicalism, or Something Near Enough, pp.44-45)

This view of the physical and biological world as made up of isolatable and discrete events is most simplistic. An "event" is singled out by a human observer. Its "cause" is arbitrarily abstracted from complex processes with enormous numbers of possible causes.

Emergence Denied

Prominent philosophers of science - committed to the ability of physical science to explain everything as "unified science" - were confident that "emergence" would go the way of "holism" and "vitalism."

Inseparably connected with holism and the Gestalt philosophy is the
doctrine of emergence. The old slogan "the whole is greater than
the sum of its parts" has of course no very clear meaning. Much of its
obscurity is due to the lack of a definition of the phrase "the sum of the
parts". Recent analyses of the still controversial significance of "organic wholeness" and of "emergent novelty" have contributed a great
deal to the clarification of the issues. There is no imperative need for
us to enter into details here. It will be sufficient for our concerns to
realize that in modern natural science no sharp distinction can be made
between resultants (as in the composition, i.e. vectorial addition of
forces or velocities) and emergents. In the explanation of the properties and the behavior of complexes and wholes we always need laws of
composition—be they as simple as the straightforward arithmetical addition of volumes, masses, electric charges, etc., or slightly more complicated as is vector addition, (or just a trifle more involved as is the
relativistic "addition" formula for velocities), or extremely complex as
are the so far not fully formulated composition laws which would be
required for the prediction of the behavior of organisms on the basis
of a complete knowledge of their microstructure and the dynamic laws
interrelating their component micro-constituents.

Modern quantum physics, on a very basic level, employs laws which
have "organismic" character, as for instance the exclusion principle of
W. Pauli which holds even for single atoms. It is conceivable that
much of what is called "emergent novelty" on the chemical and biological levels of complexity may ultimately be explained in terms of
the organismic or holistic features of the laws of atomic and molecular
dynamics; and that, given those basic micro-laws, the only composition
laws (which scientists often take for granted like "silent partners") are
simply the postulates and theorems of geometry and kinematics. This
is indeed my own, admittedly risky and speculative, guess; that is to
say, I believe that once quantum dynamics is able to explain the facts
and regularities of organic chemistry (i.e. of non-living, but complex
compounds) it will in principle also be capable of explaining the facts
and regularities of organic life.

("The 'Mental' and the 'Physical'", in Concepts, Theories, and the Mind-Body Problem, Minnesota Studies in the Philosophy of Science, vol.2, p. 414)

The Three Kinds of Information Emergence

Note there are three distinct kinds of emergence:

the order out of chaos when the matter in the universe forms information structures

the order out of order when the material information structures form self-replicating biological information structures

the pure information out of order when organisms with minds externalize information, communicating it to other minds and storing it in the environment

Information philosophy claims that everything created since the origin of the universe over thirteen billion years ago has involved just two fundamental physical processes that combine to form the core of all creative processes.

This two-step core creative process underlies the formation of microscopic objects like atoms and molecules, as well as macroscopic objects like galaxies, stars, and planets. (Note that the formation of self-organizing physical systems in conditions far from equilibrium that are the subjects of chaos and complexity theories are this basic, non-teleonomic form of emergence.)

With the emergence of teleonomic (purposive) information in self-replicating systems, the same core process underlies all biological creation. But now some random changes in information structures are rejected by natural selection, while others reproduce successfully.

Finally, with the emergence of self-aware organisms and the creation of extra-biological information stored in the environment, the same information-generating core process underlies communication, consciousness, free will, and creativity.